Our favorite place in/around Venice was the little island of Torcello. But on a short stay like yours, I guess you have to see the major sights - you definitely wouldn't want to miss San Marco. Immediately to the mainland of Venice is a rather industrial area, and you'd probably lose a lot of time trying to get to and from someplace nice to ride. One thing I did notice about Venice proper, that I hadn't thought about before we got there, was the complete absence of adult bicycles (for the same reason that there are no other wheeled vehicles there). You will see small children on bikes in and around via Garibaldi and Biennale park, but seven or eight seems to be about the limit where the kids and their bikes outgrow the tiny islands.
+1 on just exercising common sense and situational awareness to prevent theft. My mom had her purse picked in a very elaborate distraction scheme in Vienna. Tourist cities are tourist cities, and from what little I've seen in two trips and five cities, I don't think Italy deserves the reputation it has among some Americans.
Speed comes from what you put behind you. - Judi Ketteler